Tensors and General Relativity

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Discussion Overview

The discussion revolves around the prerequisites for understanding tensors in the context of general relativity (GR) and recommendations for resources to learn about tensors. Participants explore the depth of knowledge required and the suitability of various textbooks for beginners in GR and cosmology.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant questions the depth of understanding of tensors needed to study the mathematics behind general relativity.
  • Another participant suggests that many GR texts, such as Carroll's "Spacetime and Geometry," do not require prior knowledge of tensors and introduce the topic themselves.
  • It is proposed that a basic understanding of linear maps is sufficient to begin studying GR.
  • A participant notes that the rigor of the GR textbook influences the prerequisite knowledge required, indicating that more foundational and rigorous texts demand a deeper understanding of tensors.
  • Some participants recommend specific introductory texts for GR, such as Hartle and Schutz, while noting that these do not delve deeply into the mathematical foundations.
  • One participant mentions studying cosmology and expresses concern about the assumed knowledge of GR and tensors in their chosen textbook.
  • Another participant suggests utilizing online lecture notes that introduce tensor algebra and calculus in the context of GR if the chosen textbook does not cover these topics adequately.
  • A free online version of Carroll's textbook is shared as a resource.

Areas of Agreement / Disagreement

Participants generally agree that a basic understanding of tensors is sufficient to start studying GR, but there is no consensus on the specific depth of knowledge required, as it varies depending on the textbook and the level of rigor desired.

Contextual Notes

Some participants highlight that the rigor and foundational depth of GR texts can significantly influence the prerequisites, indicating a potential variability in the required understanding of tensors.

pierce15
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Hello all,

I will preface this post with an apology for not putting it in the math/science learning materials section. This would have been the best place to post my question, but for some reason I can't post there.

My question is the following: what depth of understanding must I have of tensors in order to start going through the math behind general relativity? Also, if anyone knows of any particularly good books for learning about tensors, feel free to share them. (I bought this book: https://www.amazon.com/dp/0486658406/?tag=pfamazon01-20, but I'm having a terribly difficult time following it; I strongly agree with the reviewer who wrote that he got lost in the gallimaufry of summations).

Edit: sorry for typos
 
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Most texts on General Relativity (eg Carroll's Spacetime and Geometry) don't assume a knowledge of tensors and instead introduce the topic themselves.

The knowledge of tensors you need to start doing GR is very, very simple. If you know what a linear map is you're halfway there. Carroll on spends a few pages on the subject, and IMO that's all you really need. It's not necessary to buy a whole book on the subject.
 
Thanks for the reply. I'll look into that textbook
 
piercebeatz said:
My question is the following: what depth of understanding must I have of tensors in order to start going through the math behind general relativity?

This depends on how rigorous the GR textbook you want to use actually is and how deep into the foundations of GR you want to go-more foundational topics and more rigorous textbooks will make heavier prerequisite demands of the reader.

For an introduction to GR, say at the level of Hartle, Schutz, or Carroll (Carroll is slightly higher level than Schutz) you don't need to worry much (if at all) about the math in the text, you can just jump right in. Hartle is my most favorite introductory GR text with Schutz coming in a very close second. However none of the three aforementioned texts go very deep into the foundations of GR and certainly none of them are mathematically rigorous.
 
Well if that book by itself doesn't introduce tensor algebra and tensor calculus (i.e. it presupposes knowledge of them) then you can always make use of the numerous GR lecture notes available online that do introduce these tools in the context of GR. Here's a personal favorite of mine: http://www.physics.uoguelph.ca/~poisson/research/agr.pdf (it's not rigorous but it covers all the necessary tools and concepts).
 

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